Orderly representation of the physical environment in the form of "cortical maps" is a prominent feature of the mammalian brain. In particular, in the primary visual cortex, neurons with similar response properties are clustered into respective iso-functional domains. Spatial layout, development, and function of cortical maps have been studied extensively using a variety of techniques in the past. Despite their enormous success, the use of the traditional mapping techniques is hampered by practical constraints: lack of sufficient field of view (intra- and extracellular recordings); impossibility of in vivo mapping (2-deoxyglucose); and loss of depth information (optical imaging). The rapid development of functional Magnetic Resonance Imaging (fMRI) raises the possibilities to map the functional architecture of the living brain without such limitations. The crucial question is, however, whether the spatial resolution of fMRI is ultimately sufficient to label the computational "scaffold" of the brain's functional architecture: that of columns and maps. Based on our preliminary data, we hypothesize that columnar- and layer-specific functional activity in the cortex can be imaged using hemodynamic magnetic resonance contrasts under ultra high magnetic fields (at 9.4 Tesla). It will be exciting to explore the potentials of this novel technique to elucidate the structure, function, and maps in animals and humans.